Re: FindRoot

*To*: mathgroup at smc.vnet.net*Subject*: [mg70389] Re: [mg70356] FindRoot*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Sun, 15 Oct 2006 00:18:57 -0400 (EDT)*References*: <200610140706.DAA07906@smc.vnet.net>

Putting a Print statement there to print x at each evaluation is like using something in System`Dump` or Experimental`. It might work in one version, but change in another. There are even some things that are documented to work in Mathematica that don't (four argument form of Infix anyone?). Why expect the undocumented things to work across versions? :-] And yes, MathGroupers, I am going to keep mentioning the four argument form of Infix until someone shows me how to use it or I get tired. On 10/14/06, dimmechan at yahoo.com <dimmechan at yahoo.com> wrote: > Hello. > > Let me deal with something elementary but yet confusing for me. > > Consider the equation cos(x)=x. > > FindRoot[Cos[x] == x, {x, 5}] > {x -> 0.7390851332151607} > > This prints the value of x every time a step is taken. > > FindRoot[Cos[x] == x, {x, 5}, StepMonitor :> Print[x]] > > This gives a list of the steps taken. > > Reap[FindRoot[Cos[x] == x, {x, 5}, StepMonitor :> Sow[x]]] > {{x -> 0.7390851332151607}, {{-1., -0.02837830412204312, > 1.0296174587519653, 0.7525886779802748, 0.7391248287000711, > 0.7390851335630761, 0.7390851332151607}}} > > This counts the steps. > > Block[{st = 0}, {FindRoot[Cos[x] == x, {x, 5}, StepMonitor :> st++], > st}] > {{x -> 0.7390851332151607}, 7} > > I want to know what exactly the following command gives. > > Reap[FindRoot[Cos[x] == x, {x, 5}, EvaluationMonitor :> Sow[x]]] > {{x -> 0.7390851332151607}, {{5., -54.99999999999999, -1., > 8.716216958779569, > -0.02837830412204312, 1.0296174587519653, 0.7525886779802748, > 0.7391248287000711, 0.7390851335630761, 0.7390851332151607}}} > > In versions earlier than 5.0 you could use the following command > > FindRoot[Print[x]; Cos[x] == x, {x, 5}] > > Why it cannot be used now? > > Thanks in advance for any help. > > -- http://chris.chiasson.name/

**References**:**FindRoot***From:*dimmechan@yahoo.com